Abstract:
For mixed type equation with two perpendicular singularity lines, we consider one boundary problem in the domain whose elliptic and hyperbolic part is rectangle and vertical half-strip, respectively. This problem differs from the Dirichlet problem by the fact that at the left boundary of the rectangle and of half-strip we specify not the unknown function, but the order of zero. We prove uniqueness of boundary problem solution by a spectral method with the use of Fourier–Bessel series. We give substantiation of uniform convergence of corresponding series with some restrictions upon the conditions of the problem.
Keywords:
mixed type equations, equation with singular coefficients, spectral method, Fourier–Bessel series, Bessel functions.
Citation:
A. A. Abashkin, “Solving one boundary-value problem for mixed type equation with two singular lines with the use of spectral method”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 2, 3–9; Russian Math. (Iz. VUZ), 60:2 (2016), 1–6
\Bibitem{Aba16}
\by A.~A.~Abashkin
\paper Solving one boundary-value problem for mixed type equation with two singular lines with the use of spectral method
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 2
\pages 3--9
\mathnet{http://mi.mathnet.ru/ivm9075}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 2
\pages 1--6
\crossref{https://doi.org/10.3103/S1066369X16020018}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84956545361}
Linking options:
https://www.mathnet.ru/eng/ivm9075
https://www.mathnet.ru/eng/ivm/y2016/i2/p3
This publication is cited in the following 1 articles:
Yu. E. Senitsky, E. N. Elekina, “In the consideration of internal friction forces in nonstationary dynamics problems”, RSP 2017 – XXVI R-S-P Seminar 2017 Theoretical Foundation of Civil Engineering, MATEC Web of Conferences, 117, eds. S. Jemiolo, A. Zbiciak, M. Mitew-Czajewska, M. Krzeminski, M. Gajewski, EDP Sciences, 2017, UNSP 00150
Citation in format AMSBIB
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